Last updated: 2026-06-14

Understanding the combined gas law

The combined gas law describes how a fixed amount of gas behaves when its pressure, volume, and temperature all change at once. It merges three simpler gas laws into a single relationship, making it the go-to tool whenever a gas moves between two sets of conditions — a weather balloon rising into colder, thinner air, or a sealed canister warming in the sun.

The combined gas law formula

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

Symbol	Quantity	Unit (this calculator)
P₁, P₂	Pressure (states 1, 2)	atm
V₁, V₂	Volume (states 1, 2)	L
T₁, T₂	Absolute temperature	K

Because both sides describe the same gas, the amount n and the gas constant R cancel and never appear. Rearranging lets you solve for any one of the six quantities — for example:

$$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}, \qquad V_2 = \frac{P_1 V_1 T_2}{T_1 P_2}, \qquad T_2 = \frac{T_1 P_2 V_2}{P_1 V_1}$$

Worked example

A 1.0 L sample of gas at 1.0 atm and 273 K (0 °C) is compressed to 0.50 L and heated to 546 K. What is the new pressure?

$$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2} = \frac{1.0 \times 1.0 \times 546}{273 \times 0.50} = 4.0\ \text{atm}$$

Halving the volume doubles the pressure, and doubling the absolute temperature doubles it again — giving four times the original pressure.

The three laws inside it

Hold one variable constant and the combined gas law collapses to a familiar special case:

Constant	Resulting law	Relationship
Temperature	Boyle's law	P₁V₁ = P₂V₂
Pressure	Charles's law	V₁ ÷ T₁ = V₂ ÷ T₂
Volume	Gay-Lussac's law	P₁ ÷ T₁ = P₂ ÷ T₂

To use this calculator for any of them, enter the same value for the quantity that stays constant in both states.

Always use absolute temperature

The law is a proportion, so it only works on a temperature scale that begins at true zero. Celsius and Fahrenheit have arbitrary zero points and give wrong ratios — going from 10 °C to 20 °C is not doubling the thermal energy. The Kelvin scale starts at absolute zero (−273.15 °C), so kelvin ratios are physically meaningful. This calculator accepts Celsius or Fahrenheit and converts to kelvin before computing.

Combined vs. ideal gas law

Use the combined gas law to compare two states of the same gas, when the amount stays fixed and you do not need n. Use the ideal gas law (PV = nRT) for a single state when you need an absolute quantity such as the number of moles or the mass of gas present.

Frequently Asked Questions (FAQ)

What is the combined gas law?

The combined gas law states that for a fixed amount of gas, P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂. It links the pressure, volume, and absolute temperature of a gas between two states. Given any five of the six values, you can solve for the sixth. Temperature must always be in kelvin, because the law relies on an absolute temperature scale.

How is the combined gas law different from the ideal gas law?

The ideal gas law (PV = nRT) describes a single state of a gas and includes the amount n and the gas constant R. The combined gas law compares two states of the same fixed amount of gas, so n and R cancel out and never appear. Use the combined gas law when a gas changes conditions — for example, a balloon moving from warm to cold air — and the ideal gas law when you need an absolute quantity such as the number of moles.

How does it relate to Boyle’s, Charles’s, and Gay-Lussac’s laws?

The combined gas law contains all three as special cases. Hold temperature constant (T₁ = T₂) and it reduces to Boyle’s law, P₁V₁ = P₂V₂. Hold pressure constant and it becomes Charles’s law, V₁ ÷ T₁ = V₂ ÷ T₂. Hold volume constant and it becomes Gay-Lussac’s law, P₁ ÷ T₁ = P₂ ÷ T₂. To use this calculator for one of those, simply enter the same value for the quantity that stays constant in both states.

Why must temperature be in kelvin?

Gas laws are proportional relationships, and proportions only work on a scale that starts at true zero. The Celsius and Fahrenheit scales have arbitrary zero points, so using them gives wrong ratios — doubling from 10 °C to 20 °C is not doubling the thermal energy.

The Kelvin scale starts at absolute zero, so a doubling of kelvin really is a doubling of the quantity. This calculator accepts Celsius or Fahrenheit and converts to kelvin before computing.